On Sat, 16 Feb 2008 17:47:39 -0800, Mark Dickinson wrote:
> I've no clue where your (Steven's) idea that 'all ordinals are surreal
> numbers' came from. They're totally unrelated.
Tell that to John Conway.
[quote]
Just as the *real* numbers fill in the gaps between the integers, the
*surreal* numbers fill in the gaps between Cantor's ordinal numbers. We
get them by generalizing our use of the {|} notation for the ordinal
numbers.
[...]
The ordinal numbers are those where there aren't any numbers to the right
of the bar:
{|} = 0, the simplest number of all
{0|} = 1, the simplest number greater than 0
{0,1|} = 2, the simplest number greater than 1 (and 0)
and so on.
[end quote]
"The Book of Numbers", John W Conway and Richard K Guy, Copernicus Books,
1996, p.283.
I trust I don't have to explain this to Mark, but for the benefit of
anyone else reading, Conway invented surreal numbers.
--
Steven
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